You may also like

problem icon

Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

problem icon

Six Discs

Six circular discs are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box. Can you put the boxes in order according to the areas of their bases?

problem icon

Quadarc

Given a square ABCD of sides 10 cm, and using the corners as centres, construct four quadrants with radius 10 cm each inside the square. The four arcs intersect at P, Q, R and S. Find the area enclosed by PQRS.

Inscribed in a Circle

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The area of a square inscribed in a circle with a unit radius is, satisfyingly, $2$.

What is the area of a regular hexagon inscribed in a circle with a unit radius?

 

What is the area of an equilateral triangle inscribed in a circle with a unit radius?


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
Copyright © 1997 - 2017. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.